PART C: Answer only 1 of the questions C. 1 - C. 2. Do not answer additional questions. This part is worth 55% of the exam.

C. 1. Outline the structure of an input-output model (including assumptions about supply and demand). What is an inverse matrix? Why is inverting a matrix significant in terms of input-output analysis?

C. 2. Describe a Linear Programming (LP) Problem. Specifically, describe (you can use an example):

- Primal Linear Programming Problem

- Dual Linear Programming Problem

- Interpretation of the Primal Linear Programming Problem

- Interpretation of the Dual Linear Programming Problem

Input and output is important because sometimes the demands of a product are not being met. When this happens, companies may need to create more products to satisfy a shortage, or decrease productivity when there is a surplus.

Macroeconomic analysis based on the interdependencies between economic sectors or industries shows the input output model.

Explanation:

The Input-Output (IPO) Model is a functional graph that identifies the inputs, outputs, and required processing tasks required to transform inputs into outputs. The inputs represent the flow of data and materials into the process from the outside.

This analysis is based on the following assumptions:

The whole economy is divided into two sectors-"inter-industry sectors" and "final-demand sectors," both being capable of sub-sectoral division. The total output of any inter-industry sector is generally capable of being used as inputs by other inter-industry sectors, by itself and by final demand sectors No two products are produced jointly. Each industry produces only one homogeneous product. Prices, consumer demands and factor supplies are given. There are constant returns to scale.

In linear algebra, an n-by-n square matrix A is called invertible if there exists an n-by-n square matrix B such that where Iₙ denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. Statistics on inverse matrix coefficients for input-output tables within the domestic market describing the sale and purchase relationships between producers and consumers within an economy. They can be produced by illustrating flows between the sales and purchases of industry outputs or by illustrating the sales and purchases of product outputs.